A study of influence of diffusion inside a spherical shell under thermoelastic diffusion with relaxation times

Abstract

The present work is concerned with the elasto-thermo-diffusion interactions inside a spherical shell whose inner and outer boundaries are traction free and are subjected to a step input in temperature under generalized thermoelastic diffusion. The chemical potential is also assumed to be a function of time on the boundaries of the shell. The problem is studied by employing three different theories of thermoelastic diffusion in a unified way. The integral transform technique is used to obtain the general solution. Using a numerical method and computer programming, the final solution in the physical domain is obtained. The results corresponding to thermoelastic medium, that is, in the absence of diffusion, are also found in a particular case. The influence of diffusion on variation of physical fields due to the cross effects arising from the coupling of temperature, diffusion and strain fields inside the shell is analyzed with the help of graphically plotted results of different field variables in the thermoelastic medium and thermoelastic diffusive medium. The variation of this influence with time under different theories is also discussed. The significant points are highlighted.